# Understanding Lucky Dough Chances

- The Lucky Dough game consists of a square with nine boxes.
- The player selects a number from 1 to 5 in each of the eight boxes; the center box is always a free match.
- The more lines a player matches, the bigger the prize.

### You Can Calculate the Odds of Winning Lucky Dough.

To calculate the odds of winning the game, here are a few terms you'll need to know:

**F = Field Size**, or the number of numbers that can be drawn in any box. In this case, it is always 5.

N = Number of Fields, or the number of boxes in the game. It's always 8 in this game, since the center box is

always a free match.

**M = Number of Fields Not Matched**, or missed fields.

**P = Number of Permutations**, or possible outcomes that can result from a drawing.

**C = Combinations** that form a line.

**^ = Symbol representing an exponential**; directs us to raise that number to the nth power.

For example, 3^ means 3 x 3 x 3, or 3 to the 3rd power.

*** = Symbol representing multiplication**.

For example, 3*3 means 3 multiplied by 3.

**/ = Symbol representing division**.

### So, let's get started.

The basic formula for calculating the odds of winning in a combinatorial line game looks like this:

For any prize level, say three lines, there are numerous combinations of outcomes that can form a line. For example, 14 ways to match in 6 of 8 boxes and form 3 winning lines and 16 ways to match 5 of 8 boxes and form 3 winning lines. When there are numerous combinations possible, they are added together in the numerator of the probability formula.

### Let's work through an example.

It may look hard, but it really isn't. We can find the odds of winning 3 lines by plugging the numbers into the formula above. It looks like this:

**(((5-1)^2)*14+((5-1)^3)*16) / (5^8)**

**((4^2*14)+(4^3*16)) / 5*8 **

*(4 squared times 14 plus 4 cubed times 16 divided by 5 to the eighth power)*

**((16 times 14) plus (64 times 16)) divided by 390,625**

**224 plus 1024 divided by 390,625**

**1248 divided by 390,625**

**=0.003195**

**The odds of winning are 1/.003195**

**or 313 to 1**

You can calculate the odds for other outcomes using this example as your guide.

For any questions regarding the above information, please feel free to contact our Research & Development Division.

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